Precalculus

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The 8th term in an arithmetic sequence is 5, and the sum of the first 10 terms is 20. Find the common difference and the first term of the sequence.

Alright so in an arithmetic squence the difference d between any two successive numbers is constant. So if the first term is x, then the second term is (x+d), and the third term is (x+2d), etc. up to the tenth term in this case which is (x+9d). We know that the eighth term is 5 so this gives...

x+7d=5

and we know that the sum of the first ten terms is 20 which gives...

x+(x+d)+(x+2d)+(x+3d)+...+(x+9d)=20
or..
10x+45d=20

Solve these two equations for x and d..

x+7d=5
10x+45d=20

I get... d=1.2 and x=-3.4

Hope that helps

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